用广义高阶锥方向导数刻画集值优化强有效元

On Characterizations of Strongly Efficient Element of Set-Valued Optimization with Generalized Higher-Order Cone-Directed Derivatives

在实赋范线性空间中研究集值优化问题强有效元的最优性条件.利用广义高阶锥方向相依导数,在内部锥类凸假设下,给出了无约束集值优化问题强有效元的广义高阶必要条件,并在没有任何凸性假设下利用凸集分离定理得到了充分条件.

The optimality conditions of strongly efficient element of set-valued optimization have been con-sidered in real normed spaces.By employing the generalized higher-order cone-directed contingent deriva-tive introduced by Wang ect,under the assumption of the ic-cone-convexlikeness,the generalized higher-order necessary condition of strongly efficient element of unconstrained set-valued optimization has bene given,and sufficient condition been obtained without any convexity assumption by the separate theorem of convex sets.